They are not, as critics have said, "mere unorganised explosions of random energy".

Pollock, who died in 1956, created many of his works by dripping spirals of paint over vast canvasses. He believed they contained "pure harmony" but there has been an enduring controversy over how intentional the finished product was.

Figure 1948-9: relatively simple

But now a group from the Physics Department of the University of New South Wales, Australia, have shown that his paintings possess fractal properties.

Natural patterns

Fractals are a mathematical way of describing the underlying pattern in apparently chaotic patterns. They are common patterns in nature, in leaves, weather patterns and galaxies.

A key feature of fractal patterns is that they look the same and as complex whether the whole pattern is viewed or just a detail.

The scientists analysed the paintings Pollock produced between 1943 to 1952. Their work shows that the fractal dimension, a measure of the complexity, increased steadily over that time from a relatively simple value near one to 1.72.

They believe that this approach could provide a "quantitative, objective technique to both validate and date Pollock's drip paintings".

White Light, 1954: a high fractal dimension

But the mathematical calculations also reveal how the artist refined his dripping method. In 1943, he used single squiggles of paint that only covered 20% of the canvas. By 1952, multiple squiggles covered over 90% of each painting.

Mignon Nixon is a lecturer in American art at London's Courtauld Institute and told BBC News Online that Pollock's intentions is still a hot issue.

"Mathematical models may be a way of attributing a kind of mastery and order, by shifting from an aesthetic, subjective mode of examination to a more objective, scientific one."

She says scientific approaches can be useful in the study of art. "If you want to know how was a painting was made or how do we date it, then technical help is crucial.

"But the information you get that way is also useful for interpretation because you know more about how the thing was made."

No mess

What Pollock himself would have thought of the work can only be guessed but part of his 1947-48 statement in Possibilities suggests he might not have been too surprised.

"The painting has a life of its own. I try to let it come through. It is only when I lose contact with the painting that the result is a mess. Otherwise there is pure harmony, an easy give and take, and the painting comes out well."

The fractal research is published in the journal Nature.